I was wondering when you say “many different ways to tie white” what are some ways other than Ashkenazinic and Chabad?

Yes there are many, many ties to tie white. Here are a few that are listed in R. Tavger’s book on tzitzit “Klil Tekhelet”:

Tying methods in white:
– Common 7-8-11-13
– Hida 10-5-6-5 (Y-K-V-K)
– Lekach Tov 7-7-7-7
– HaMaspik L’Ovdei Hashem 7 chulyot of 3 winds (like Rambam)
– Meiri Yevamot:
knot
7 (teimani) chulyot
knot
7 (teimani) chulyot
knot
7 (teimani) chulyot
knot
7 or 13 (teimani) chulyot
knot
– Tzfunot
knot
2 (teimani) chulyot
knot
7 (teimani) chulyot
knot
2 (teimani) chulyot
knot
2 (teimani) chulyot
knot
– Beit Yosef 7-9-11-13

– Itur (Hil. Tz. p.69a) brings a method:
knot
7 wraps
knot

– Itur (Hil. Tz. p.69a) brings a method:
7 knots
70 wraps
double knot

– Mois Navon.